Subgroup classification in Out(F_n)

Abstract

For any subgroup H of Out(F_n), either H has a finite index subgroup that fixes the conjugacy class of some proper, nontrivial free factor of F_n, or H contains a fully irreducible element phi, meaning that no positive power of phi fixes the conjugacy class of any proper, nontrivial free factor of F_n.

83 pages

References in corpus (2)

• A hyperbolic Out(F_n)-complex
• The Recognition Theorem for Out(F_n)

Cited by in corpus (11)

• The Tits alternative for the automorphism group of a free product
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• A short proof of Handel and Mosher's alternative for subgroups of $\text{Out}(F_N)$
• Subgroup decomposition in $\text{Out}(F_n)$, Part IV: Relatively irreducible subgroups
• Regluing graphs of Free Groups
• Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups
• A recipe for short-word pseudo-Anosovs
• Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell
• Incoherence of free-by-free and surface-by-free groups